Difficult problem involving factorials and binomial expansion. Can anyone help me?

• Nov 13th 2010, 11:47 PM
mm19
Difficult problem involving factorials and binomial expansion. Can anyone help me?
Given that n is a positive integer and that a and b are real constants, find a and bi if :

(1+ax)^n=1-6x+(81/5)x^2+bx^3+……….

Hint: You must solve for n first

A step by step explanation would be greatly appreciated. This question really has me stumped and the teacher's explanation didn't help.
• Nov 14th 2010, 12:01 AM
Debsta
Write down the first few terms of (1+ax)^n
• Nov 14th 2010, 12:52 AM
mm19
Okay. I think this is what you mean.

1-6x+(81/5)x^2+bx^3+............
• Nov 14th 2010, 12:56 AM
mr fantastic
Quote:

Originally Posted by mm19
Okay. I think this is what you mean.

1-6x+(81/5)x^2+bx^3+............

All you have done is written out the right hand side! Exactly how do you think that will help? You were told to "Write down the first few terms of (1+ax)^n" - with the expectation that you would do so by expanding it using the binomial theorem!
• Nov 14th 2010, 09:48 AM
mm19
Sorry I got confused on what he meant.

nC1 (1)^(n-1) (ax)^1
nC2 (1)^(n-2) (ax)^2
nC3 (1)^(n-3) (ax)^3

I'm assuming this is what he means.
• Nov 14th 2010, 10:07 AM
mr fantastic
Quote:

Originally Posted by mm19
Sorry I got confused on what he meant.

nC1 (1)^(n-1) (ax)^1
nC2 (1)^(n-2) (ax)^2
nC3 (1)^(n-3) (ax)^3

I'm assuming this is what he means.

What about the "r = 0" term?

Now what you do is equate the coefficients of powers of x on each side of the expression given in the question and draw a conclusion.
• Nov 14th 2010, 12:51 PM
Debsta
To mm19....."she" means not "he" means!!